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Approximate Boltzmann Distributions in Quantum Approximate Optimization

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arXiv 2022年

作者： Lotshaw, Phillip C. Siopsis, George Ostrowski, James Herrman, Rebekah Alam, Rizwanul Powers, Sarah Humble, Travis S. Quantum Computational Science Group Oak Ridge National Laboratory Oak RidgeTN37381 United States Department of Physics and Astronomy University of Tennessee KnoxvilleTN37996-1200 United States Department of Industrial and Systems Engineering University of Tennessee KnoxvilleTN37996-2315 United States Computer Science and Mathematics Division Oak Ridge National Laboratory Oak RidgeTN37381 United States Quantum Science Center Oak Ridge National Laboratory Oak RidgeTN37381 United States

Approaches to compute or estimate the output probability distributions from the quantum approximate optimization algorithm (QAOA) are needed to assess the likelihood it will obtain a quantum computational advantage. We analyze output from QAOA circuits solving 7,200 random MaxCut instances, with n = 14 − 23 qubits and depth parameter p ≤ 12, and find that the average basis state probabilities follow approximate Boltzmann distributions: The average probabilities scale exponentially with their energy (cut value), with a peak at the optimal solution. We describe the rate of exponential scaling or "effective temperature" in terms of a series with a leading order term T ~ Cmin/n√p, with Cmin the optimal solution energy. Using this scaling we generate approximate output distributions with up to 38 qubits and find these give accurate accounts of important performance metrics in cases we can simulate exactly. © 2022, CC BY-NC-ND.

关键词： Optimal systems

Modeling buried object brightness and visibility for ground penetrating radar

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arXiv 2021年

作者： Stevenson, Garrett A. Wilson, Jason Worthmann, Brian M. Xavier, Wlamir The Computational Engineering Division Lawrence Livermore National Laboratory The Department of Mathematics and Computer Science Biola University The Biola Quantitative Consulting Center The Biola Quantitative Consulting Center Biola University La MiradaCA90639 United States

Comparing the observed brightness of various buried objects is a straightforward way to characterize the performance of a ground penetrating radar (GPR) system. However, a limitation arises. A simple comparison of buried object brightness values does not disentangle the effects of the GPR system itself from the system's operating environment and the objects being observed. Therefore, with brightness values exhibiting an unknown synthesis of systemic, environmental, and object factors, GPR system analysis becomes a convoluted affair. In this work, we use an experimentally collected dataset of over 25,000 object observations from five different multi-static radar arrays to develop models of buried object brightness and control for these various effects. Our modeling efforts provide a means for quantifying the relative brightness of GPR systems, the objects they detect, and the physical properties of those objects which influence observed brightness. To evaluate the models' performance on new object observations, we repeatedly simulate fitting them to half the dataset and predicting the observed brightness values of the unseen half. Additionally, we introduce a method for estimating the probability that individual observations constitute a visible object, which aids in failure analysis, performance characterization, and dataset cleaning. © 2021, CC BY-NC-ND.

关键词： Ground penetrating radar systems

Development, Validation and Field Assessment of a Multiplex-Tandem RT-PCR for the Detection of Bovine Respiratory Disease Complex

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SSRN

SSRN 2023年

作者： Fergusson, Megan Maley, Madeleine Geraghty, Timothy Albaladejo, Javier Palarea Mason, Colin Rocchi, Mara S. SRUC Veterinary and Analytical Services Pentland Science Park Bush Loan Road EdinburghEH26 0PZ United Kingdom Moredun Research Institute Pentlands Science Park Bush Loan PenicuikEH26 0PZ United Kingdom Department of Computer Sciences Applied Mathematics and Statistics University of Girona Girona17003 Spain Biomathematics and Statistics Scotland The King’s Buildings Peter Guthrie Tait Road EdinburghEH9 3FD United Kingdom

The welfare and economic impact of bovine respiratory disease complex (BRDC), as well as the associated antibiotic usage, is one of the major challenges to the cattle-rearing industry. Accurate outbreak diagnosis, especially at etiological level, is important to inform appropriate treatment plans and long-term management strategies, such as vaccine selection. The conventional diagnostic approaches, however, have several limitations, including high costs, long turnaround times and difficult interpretation, which might delay treatment decisions, leading to the unnecessary loss of many animals. We describe the development and validation of a multiplex-tandem (MT) reverse transcription-polymerase chain reaction (RT-PCR) for the detection of seven common pathogens associated with BRDC. This test has the potential to advance pathogens identification and to overcome many of the limitations of the current testing methods. The test requires a single sample and results are obtained quickly and are not influenced by prior antimicrobial therapy or overgrowth of contaminating organisms. We demonstrate good analytical and diagnostic test characteristics for this new test, which will be a useful addition to advance the investigation and diagnosis of BRDC. © 2023, The Authors. All rights reserved.

关键词： Diagnosis

Automated Grain Boundary Detection for Bright-Field Transmission Electron Microscopy Images via U-Net

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arXiv 2023年

作者： Patrick, Matthew J. Eckstein, James K. Lopez, Javier R. Toderas, Silvia Asher, Sarah A. Whang, Sylvia I. Levine, Stacey Rickman, Jeffrey M. Barmak, Katayun Department of Applied Physics and Applied Mathematics Columbia University 200 S.W. Mudd Building 500 W. 120 Street New YorkNY10027 United States Department of Physics University of Illinois 1110 W. Green Street UrbanaIL61801 United States Department of Mechanical Engineering Columbia University 210 S.W. Mudd Building 500 W. 120 Street New YorkNY10027 United States Department of Physics Barnard College 504A Altschul Hall 3009 Broadway New YorkNY10027 United States Department of Mathematics and Computer Science Duquesne University 440 College Hall 1100 Locust Street PittsburghPA15282 United States Department of Materials Science and Engineering Lehigh University Whitaker Lab 244 5 E. Packer Avenue BethlehemPA18015 United States

Quantification of microstructures is crucial for understanding processing-structure and structure-property relationships in polycrystalline materials. Delineating grain boundaries in bright-field transmission electron micrographs, however, is challenging due to complex diffraction contrast in images. Conventional edge detection algorithms are inadequate;instead, manual tracing is usually required. This study demonstrates the first successful machine learning approach for grain boundary detection in bright-field transmission electron micrographs. The proposed methodology uses a U-Net convolutional neural network trained on carefully constructed data from bright-field images and hand tracings available from prior studies, combined with targeted postprocessing algorithms to preserve fine features of interest. The image processing pipeline accurately estimates grain boundary positions, avoiding segmentation in regions with intragrain contrast and identifying low-contrast boundaries. Our approach is validated by directly comparing microstructural markers (i.e., grain centroids) identified in U-Net predictions with those identified in hand tracings;furthermore, the grain size distributions obtained from the two techniques show notable overlap when compared using t-test, Kolmogorov-Smirnov test, and Cramér-von Mises test. The technique is then successfully applied to interpret new microstructures having different image characteristics from the training data, with preliminary results from platinum and palladium microstructures presented, highlighting the versatility of our approach for grain boundary identification in bright-field micrographs. © 2023, CC BY-NC-ND.

关键词： Grain boundaries

ON THE KERNEL OF THE (κ,a)-GENERALIZED FOURIER TRANSFORM

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arXiv 2022年

作者： Gorbachev, Dmitry V. Ivanov, V.I. Tikhonov, S.Y.U. Tula State University Department of Applied Mathematics and Computer Science Tula300012 Russia Centre de Recerca Matemàtica Campus de Bellaterra Edifici C Bellaterra Barcelona08193 Spain ICREA Universitat Autònoma de Barcelona Pg. Lluís Companys 23 Barcelona08010 Spain

For the kernel Bκ,a(x, y) of the (κ, a)-generalized Fourier transform Fκ,a, acting in L2(Rd) with the weight |x|a-2vκ(x), where vκ is the Dunkl weight, we study the important question of when kBκ,ak∞ = Bκ,a(0, 0) = 1. The positive answer was known for d ≥ 2 and a2 ∈ N. We investigate the case d = 1 and a2 ∈ N. Moreover, we give sufficient conditions on parameters for kBκ,ak∞ > 1 to hold with d ≥ 1 and any a. We also study the image of the Schwartz space under the Fκ,a transform. In particular, we obtain that Fκ,a(S(Rd)) = S(Rd) only if a = 2. Finally, extending the Dunkl transform, we introduce non-deformed transforms generated by Fκ,a and study their main *** Codes 42B10, 33C45, 33C52 Copyright © 2022, The Authors. All rights reserved.

关键词： Fourier transforms

Statistical Recognition Method Based on Nonlinear Regression

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Mathematical Models and computer Simulations 2020年第6期12卷 996-1004页

作者： Gavrikov, B.M. Gavrikov, M.B. Pestryakova, N.V. Moscow City Oncology Hospital No. 62 Moscow Healthcare Department Moscow Russian Federation Keldysh Institute of Applied Mathematics Russian Academy of Sciences Moscow Russian Federation Federal Research Center Computer Science and Control Russian Academy of Sciences Moscow Russian Federation

Abstract: This study is devoted to the statistical method of classification based on nonlinear regression. The approaches used to implement it in solving the recognition problem of printed and handwritten characters are presented. Its implementation in assessing the health of the systems of the human body according to the parameters of peripheral blood is presented for the first time. The optimal structure of the polynomials is proposed. The properties of the probability estimates generated by the method are described. The structure of the sets used to train it is analyzed. © 2020, Pleiades Publishing, Ltd.

关键词： body system classification handwritten symbol human health condition peripheral blood polynomial regression printed symbol recognition statistical method

Positivity and convexity in incomplete cooperative games

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arXiv 2020年

作者： Černý, Martin Bok, Jan Hartman, David Hladík, Milan Department of Applied Mathematics Faculty of Mathematics and Physics Charles University Prague Czech Republic Computer Science Institute Faculty of Mathematics and Physics Charles University Prague Czech Republic Institute of Computer Science The Czech Academy of Sciences Prague Czech Republic

Incomplete cooperative games generalise the classical model of cooperative games by omitting the values of some of the coalitions. This allows to incorporate uncertainty into the model and study the underlying games as well as possible payoff distribution based only on the partial information. In this paper we perform a systematic study of incomplete games, focusing on two important classes of cooperative games: positive and convex games. Regarding positivity, we generalise previous results for a special class of minimal incomplete games to general setting. We characterise non-extendability to a positive game by the existence of a certificate and provide a description of the set of positive extensions using its extreme games. The results are then used to obtain explicit formulas for several classes of incomplete games with special structures. The second part deals with convexity. We begin with considering the case of non-negative minimal incomplete games. Then we survey existing results in the related theory of set functions, namely providing context to the problem of completing partial functions. We provide a characterisation of extendability and a full description of the set of symmetric convex extensions. The set serves as an approximation of the set of convex extensions. Finally, we outline an entirely new perspective on a connection between incomplete cooperative games and cooperative interval *** Codes 91A12 Copyright © 2020, The Authors. All rights reserved.

关键词： Game theory

Design and Experimental Evaluation of a Haptic Robot-Assisted System for Femur Fracture Surgery

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arXiv 2023年

作者： Alruwaili, Fayez H. Clancy, Michael P. Saeedi-Hosseiny, Marzieh S. Logar, Jacob A. Papachristou, Charalampos Haydel, Christopher Parvizi, Javad Iordachita, Iulian I. Abedin-Nasab, Mohammad H. The Biomedical Engineering Department Rowan University GlassboroNJ08028 United States The Electrical and Computer Engineering Department Rowan University GlassboroNJ08028 United States The College of Science & Mathematics Rowan University GlassboroNJ08028 United States Virtua Health MoorestownNJ08057 United States Rothman Orthopedic Institute Thomas Jefferson University Hospital PhiladelphiaPA United States The Laboratory for Computational Sensing and Robotics Johns Hopkins University BaltimoreMD21218 United States

In the face of challenges encountered during femur fracture surgery, such as the high rates of malalignment and X-ray exposure to operating personnel, robot-assisted surgery has emerged as an alternative to conventional state-of-the-art surgical methods. This paper introduces the development of Robossis, a haptic system for robot-assisted femur fracture surgery. Robossis comprises a 7-DOF haptic controller and a 6-DOF surgical robot. A unilateral control architecture is developed to address the kinematic mismatch and the motion transfer between the haptic controller and the Robossis surgical robot. A real-time motion control pipeline is designed to address the motion transfer and evaluated through experimental testing. The analysis illustrates that the Robossis surgical robot can adhere to the desired trajectory from the haptic controller with an average translational error of 0.32 mm and a rotational error of 0.07°. Additionally, a haptic rendering pipeline is developed to resolve the kinematic mismatch by constraining the haptic controller’s (user’s hand) movement within the permissible joint limits of the Robossis surgical robot. Lastly, in a cadaveric lab test, the Robossis system assisted surgeons during a mock femur fracture surgery. The result shows that Robossis can provide an intuitive solution for surgeons to perform femur fracture surgery. Copyright © 2023, The Authors. All rights reserved.

关键词： Robotic surgery

Optimal renormalization of multi-scale systems

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arXiv 2021年

作者： Price, Jacob Meuris, Brek Shapiro, Madelyn Stinis, Panos Pacific Northwest National Laboratory RichlandWA99354 United States Department of Mathematics and Computer Science University of Puget Sound SeattleWA98416 United States Department of Mechanical Engineering University of Washington SeattleWA98195 United States Department of Applied Mathematics University of Washington SeattleWA98195 United States

While model order reduction is a promising approach in dealing with multi-scale time-dependent systems that are too large or too expensive to simulate for long times, the resulting reduced order models can suffer from instabilities. We have recently developed a time-dependent renormalization approach to stabilize such reduced models. In the current work, we extend this framework by introducing a parameter that controls the time-decay of the memory of such models and optimally selecting this parameter based on limited fully resolved simulations. First, we demonstrate our framework on the inviscid Burgers equation whose solution develops a finite-time singularity. Our renormalized reduced order models are stable and accurate for long times while using for their calibration only data from a full order simulation before the occurrence of the singularity. Furthermore, we apply this framework to the 3D Euler equations of incompressible fluid flow, where the problem of finite-time singularity formation is still open and where brute force simulation is only feasible for short times. Our approach allows us to obtain for the first time a perturbatively renormalizable model which is stable for long times and includes all the complex effects present in the 3D Euler dynamics. We find that, in each application, the renormalization coefficients display algebraic decay with increasing resolution, and that the parameter which controls the time-decay of the memory is *** Codes 65M99, 35D30, 35B44 Copyright © 2021, The Authors. All rights reserved.

关键词： Flow of fluids